By default, electrum tries to minimize the transaction fee with the limitation that if there are multiple UTXOs in the same address, it either uses all of them or none of them.
Nope, Electrum uses random addresses to maximize your privacy if UTXOs are in different addresses that is the case with OP if I am not wrong which is the default behaviour in Electrum.
You are right that electrum tries to maximize the privacy, but what do you mean by random?
Let's say you have two UTXOs. One of them is worth 0.02 BTC and the other one is worth 0.03 BTC and they have received in different addresses. Now you want to spend 0.01 BTC without using coin control feature. Are you saying both of your UTXOs have the chance to be used by electrum? If so, no. That's not how electrum select UTXOs.
The coin selection in Electrum is both deterministic and random but with some conditions.
You have to look at the source code for the details but generally speaking Electrum creates "buckets" from your UTXOs from each address and tries to deterministically choose a "bucket" that can produce the best transaction that has the amount you want to pay and produces less blockchain bloat.